The paper is devoted to the discussion of some philosophical and historical problems connected with the theorem on the undefinability of the notion of truth. In particular the problem of the priority of proving this theorem will be considered. It is claimed that Tarski obtained this theorem independently though he made clear his indebtedness to Gödel’s methods. On the other hand, Gödel was aware of the formal undefinability of truth in 1931, but he did not publish this result. Reasons for (...) that are also considered. (shrink)

Dieser Band umfasst 35 Texte des Wiener Philosophen und Wissenschaftstheoretikers Friedrich G. Wallner aus den 1980er Jahren. Sie setzen sich allesamt auseinander mit dem sprachphilosophischen Denken des fruhen wie spaten Wittgenstein. Die Auseinandersetzung erfolgt dabei in einer zweifachen Weise: In einem ersten Teil gilt es den Texten, Grundgedanken Wittgensteins zu analysieren, zu erhellen sowie deren Pragungen und Einflusse aufzuzeigen. Dabei werden der Ansatz seines Denkens sowie dessen Bedeutung fur Wissenschaftstheorie und Dichtung erortert. In einem zweiten Teil verfolgen die Texte (...) das Ziel, im Anschluss an Wittgenstein ein Konzept von Philosophie auszuarbeiten, welches Philosophie als Therapie begreift. Ein Konzept, welches im Horizont der Einzelwissenschaften mehrfach zur Anwendung kommt.". (shrink)

Zygmunt Ratajczyk was a deep and subtle mathematician who, with mastery, used sophisticated and technically complex methods, in particular combinatorial and proof-theoretic ones. Walking always along his own paths and being immune from actual trends and fashions he hesitated to publish his results, looking endlessly for their improvement.

This volume is written jointly by Witold Marciszewski, who contributed the introductory and the three subsequent chapters, and Roman Murawski who is the author of the next ones - those concerned with the 19th century and the modern inquiries into formalization, algebraization and mechanization of reasonings. Besides the authors there are other persons, as well as institutions, to whom the book owes its coming into being. The study which resulted in this volume was carried out in the Historical Section (...) of the research project _Logical Systems and Algorithms for Automatic Testing of Reasoning,_ 1986-1990, in which participated nine Polish universities; the project was coordinated by the Department of Logic, Methodology and Philosophy of Science of the Bia??l??ystok Branch of the University of Warsaw, and supported by the Ministry of Education 1987). The major part of the project was focussed on the software for computer-aided theorem proving called Mizar MSE ) due to Dr. Andrzej Trybulec. He and other colleagues deserve a grateful mention for a hands-on experience and theoretical stimulants owed to their collaboration. (shrink)

The paper is devoted to phenomenological ideas in conceptions of modern philosophy of mathematics. Views of Husserl, Weyl, Becker andGödel will be discussed and analysed. The aim of the paper is to show the influence of phenomenological ideas on the philosophical conceptions concerning mathematics. We shall start by indicating the attachment of Edmund Husserl to mathematics and by presenting the main points of his philosophy of mathematics. Next, works of two philosophers who attempted to apply Husserl’s phenomenological ideas to the (...) philosophy of mathematics, namely Hermann Weyl and Oskar Becker, will be briefly discussed. Lastly, the connections between Husserl’s ideas and the philosophy of mathematics of Kurt Gödel will be studied. (shrink)

Published posthumously in 1908, Ecce Homo was written in 1888 and completed just a few weeks before Nietzsche’s complete mental collapse. Its outrageously egotistical review of the philosopher’s life and works—featuring chapters called Why I Am So Wise and Why I Write Such Good Books—are redeemed from mere arrogance by masterful language and ever-relevant ideas. In addition to settling scores with his many personal and philosophical enemies, Nietzsche emphasizes the importance of questioning traditional morality, establishing autonomy, and making a commitment (...) to creativity. Essential reading for students of philosophy, this unique memoir is crucial to an understanding of Nietzsche’s other works. (shrink)

In this study Friedrich Waismann gives a systematic presentation of insights into philosophical problems which can be achieved by clarifying the language in which the problems are posed. Much of the material and the method itself derive from Wittgenstein's work in the early 30s. The book was originally envisaged as a lucid and well organized account of Wittgenstein's distinctive form of linguistic philosophy to enable the Vienna Circle to incorporate these valuable methods into their own programme of analysis. The (...) project evolved over many years into a wide-ranging survey of the dissolution of many philosophical problems and the construction of a systematic philosophical grammar. Waismann shows in detail how puzzlement can be removed by careful description of the uses of the terms employed in framing problems. At the same time, he sketches a general framework for analysis of language, including chapters on names, general terms, logical operators, propositions, questions, etc. This book is an authoritative presentation of Wittgenstein's influential philosophy of language in a format much easier to follow than his own intricate and elusive texts. Waismann exhibits clearly the merits of this method of philosophizing. This book should serve as an important and useful text for those who wish to understand the method and power of linguistic philosophy. It has no equal as an introduction to Wittgenstein's philosophy. (shrink)

A central aim of cognitive science is to understand the fundamental mechanisms that enable humans to navigate and make sense of complex environments. In this letter, we argue that computational complexity theory, a foundational framework for evaluating computational resource requirements, holds significant potential in addressing this challenge. As humans possess limited cognitive resources for processing vast amounts of information, understanding how humans perform complex cognitive tasks requires comprehending the underlying factors that drive information processing demands. Computational complexity theory provides a (...) comprehensive theoretical framework to achieve this goal. By adopting this framework, we can gain new insights into how cognitive systems work and develop a more nuanced understanding of the relation between task complexity and human behavior. We provide empirical evidence supporting our argument and identify several open research questions and challenges in applying computational complexity theory to human decision‐making and cognitive science at large. (shrink)

The Origin of the Family, Private Property and the State (1884), was a provocative and profoundly influential critique of the Victorian nuclear family. Engels argued that the traditional monogamous household was in fact a recent construct, closely bound up with capitalist societies. Under this patriarchal system, women were servants and, effectively, prostitutes. Only Communism would herald the dawn of communal living and a new sexual freedom and, in turn, the role of the state would become superfluous.

Lvov-Warsaw School in Philosophy – as the very name suggests – was connected mainly with two academic centers: universities in Lvov and Warsaw. However, it had a broader impact. The members of this school were active also at other universities, in particular in Cracow, Vilnius and Poznań. The aim of the paper is to present and analyze the connections of Lvov-Warsaw School with the University in Poznań.

Nicholas of Cusa was first of all a theologian but he was interested also in mathematic and natural sciences. In fact philosophico-theological and mathematical ideas were intertwined by him, theological and philosophical ideas influenced his mathematical considerations, in particular when he considered philosophical problems connected with mathematics and vice versa, mathematical ideas and examples were used by him to explain some ideas from theology. In this paper we attempt to indicate this mutual influence. We shall concentrate on the following problems: (...) the role and place of mathematics and mathematical knowledge in knowledge in general and in particular in theological knowledge, ontology of mathematical objects and their origin, in particular their relations to God and their meaning for the description of the world and physical reality, infinity in mathematics versus infinity in theology and their mutual relations and connections. It will be shown that—according to Nicholas—mathematics and mathematical thinking are tools of rationalization of theology and liberating it in a certain sense from the trap of apophatic theology. (shrink)

The Voices of Wittgenstein brings for the first time, in both the original German and in English translation, over one hundred short essays in philosophical logic and the philosophy of mind. This text is of key historical importance to understanding Wittgenstein's philosophical thought and development in the 1930's. Transcribed from the papers of Friedrich Waismann and dating from 1932 to 1935, the majority are highly important dictations by Wittgenstein to Waismann. It also includes texts of redrafted material by Waismann, (...) closely based on these dictations. (shrink)

Buch 1. Geschichte des Materialismus bis auf Kant.--Buch 2. Geschichte des Materialismus seit Kant.

The paper is devoted to the description of life and scientific achievements as well as the influence of Seweryna Łuszczewska-Romahnowa.

A work of Nietzsche's later years, The Antichrist was written after Thus Spoke Zarathustra and shortly before the mental collapse that incapacitated him for the rest of his life. The work is both an unrestrained attack on Christianity and a further exposition of Nietzsche's will-to-power philosophy so dramatically presented in Zarathustra. Christianity, says Nietzsche, represents "everything weak, low, and botched; it has made an ideal out of antagonism towards all the self-preservative instincts of strong life." By contrast, Nietzsche defines good (...) as: "All that enhances the feeling of power, the Will to Power, and power itself in man. What is bad?-All that proceeds from weakness. What is happiness?-The feeling that power is increasing,-that resistance has been overcome." In attempting to redefine the basis of Western values by demolishing the formative influence of the Judeo-Christian tradition, The Antichrist has proved to be highly controversial and continuously stimulating to later generations of philosophers. (shrink)

The present book is an introduction to the philosophy of mathematics. It asks philosophical questions concerning fundamental concepts, constructions and methods - this is done from the standpoint of mathematical research and teaching. It looks for answers both in mathematics and in the philosophy of mathematics from their beginnings till today. The reference point of the considerations is the introducing of the reals in the 19th century that marked an epochal turn in the foundations of mathematics. In the book problems (...) connected with the concept of a number, with the infinity, the continuum and the infinitely small, with the applicability of mathematics as well as with sets, logic, provability and truth and with the axiomatic approach to mathematics are considered. In Chapter 6 the meaning of infinitesimals to mathematics and to the elements of analysis is presented. The authors of the present book are mathematicians. Their aim is to introduce mathematicians and teachers of mathematics as well as students into the philosophy of mathematics. The book is suitable also for professional philosophers as well as for students of philosophy, just because it approaches philosophy from the side of mathematics. The knowledge of mathematics needed to understand the text is elementary. Reports on historical conceptions. Thinking about today‘s mathematical doing and thinking. Recent developments. Based on the third, revised German edition. For mathematicians - students, teachers, researchers and lecturers - and readersinterested in mathematics and philosophy. Contents On the way to the reals On the history of the philosophy of mathematics On fundamental questions of the philosophy of mathematics Sets and set theories Axiomatic approach and logic Thinking and calculating infinitesimally – First nonstandard steps Retrospection. (shrink)

Roman Murawski; V*—The Development of Symbolism in Logic and its Philosophical Background, Proceedings of the Aristotelian Society, Volume 89, Issue 1, 1 June 1.

Roman Murawski; V*—The Development of Symbolism in Logic and its Philosophical Background, Proceedings of the Aristotelian Society, Volume 89, Issue 1, 1 June 1.

The paper is devoted to the presentation and analysis of the philosophical views concerning logic and mathematics of the leading members of Cracow Circle, i.e., of Jan Salamucha, Jan Franciszek Drewnowski and Józef Maria Bocheński. Their views on the problem of possible applicability of logical tools in metaphysical and theological researches is also discussed.

We present the first effectively presentable fully abstract model for Starkʼs Reduced ML, a call-by-value higher-order programming language featuring integer-valued references. The model is constructed using techniques of nominal game semantics. Its distinctive feature is the presence of carefully restricted information about the store in plays, combined with conditions concerning the participantsʼ ability to distinguish reference names. We show how it leads to an explicit characterization of program equivalence.

The aim of this book is to present and analyze philosophical conceptions concerning mathematics and logic as formulated by Polish logicians, mathematicians and philosophers in the 1920s and 1930s. It was a remarkable period in the history of Polish science, in particular in the history of Polish logic and mathematics. Therefore, it is justified to ask whether and to what extent the development of logic and mathematics was accompanied by a philosophical reflection. We try to answer those questions by analyzing (...) both works of Polish logicians and mathematicians who have a philosophical temperament as well as their research practice. Works and philosophical views of the following Polish scientists will be analyzed: Wacław Sierpiński, Zygmunt Janiszewski, Stefan Mazurkiewicz, Stefan Banach Hugo Steinhaus, Eustachy Żylińsk and Leon Chwistek, Jan Łukasiewicz, Zygmunt Zawirski, Stanisław Leśniewski, Tadeusz Kotarbiński, Kazimierz Ajdukiewicz, Alfred Tarski, Andrzej Mostowski and Henryk Mehlberg, Jan Sleszyński, Stanisław Zaremba and Witold Wilkosz. To indicate the background of scientists being active in the 1920s and 1930s we consider in Chapter 1 some predecessors, in particular: Jan Śniadecki, Józef Maria Hoene-Wroński, Samuel Dickstein and Edward Stamm. (shrink)

The present work carries us back to a period which, although chronologically no more than a generation or so behind us, has become as foreign to the present generation in Germany as if it were already a full hundred years old. Yet it was the period of Germany's preparation for the Revolution of 1848; and all that has happened in our country since then has been merely a continuation of 1848, merely the execution of the last will and testament of (...) the revolution. Just as in France in the eighteenth century, so in Germany in the nineteenth, a philosophical revolution ushered in the political collapse. But with what a difference! The French were in open combat with all official science, with the church and often also the state; their writings were printed beyond the frontier, in Holland or England, while they themselves were often on the point of landing in the Bastille. But the Germans were professors, state-appointed instructors of youth; their writings were recognized textbooks, and the system rounding off the whole development---the Hegelian system---was even raised, in some degree, to the rank of a royal Prussian philosophy of state! Was it possible that a revolution could hide behind these professors, behind their pedantically obscure phrases, their ponderous, wearisome sentences? Were not the liberals, the very people who then passed as the representatives of the revolution, the bitterest opponents of this brain-befuddling philosophy? But what neither governments nor liberals saw was seen by at least one man as early as 1833, and indeed by a man called Heinrich Heine. (shrink)

In the paper some applications of Gödel's incompleteness theorems to discussions of problems of computer science are presented. In particular the problem of relations between the mind and machine (arguments by J.J.C. Smart and J.R. Lucas) is discussed. Next Gödel's opinion on this issue is studied. Finally some interpretations of Gödel's incompleteness theorems from the point of view of the information theory are presented.

Praca poświęcona jest prezentacji i krytycznej ocenie poglądów filozoficznych Jana Franciszka Drewnowskiego na matematykę i logikę. Podstawą rozważań są cztery źródła. Podstawowym źródłem jest Drewnowskiego "Zarys programu filozoficznego", dalej dwa artykuły, a mianowicie "Stosowanie logiki symbolicznej w filozofii" oraz "Uwagi o stosowaniu logiki symbolicznej", w końcu fragmenty dziennika. Pokazuje się w niej, jak Drewnowski rozumiał matematykę i teorie matematyczne, jak widział logikę i jej rolę w nauce oraz na ile był zaznajomiony ze współczesnymi osiągnięciami w zakresie logiki matematycznej i podstaw (...) matematyki oraz z ich konsekwencjami dla filozofii matematyki. (shrink)